DAY-SIDE z -BAND EMISSION AND ECCENTRICITY OF
WASP-12b
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Citation
López-Morales, Mercedes, Jeffrey L. Coughlin, David K. Sing,
Adam Burrows, Dániel Apai, Justin C. Rogers, David S. Spiegel,
and Elisabeth R. Adams. “ DAY-SIDE z -BAND EMISSION AND
ECCENTRICITY OF WASP-12b .” The Astrophysical Journal
716, no. 1 (May 20, 2010): L36–L40. © 2010 American
Astronomical Society.
As Published
http://dx.doi.org/10.1088/2041-8205/716/1/l36
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Thu May 26 00:40:45 EDT 2016
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The Astrophysical Journal Letters, 716:L36–L40, 2010 June 10
C 2010.
doi:10.1088/2041-8205/716/1/L36
The American Astronomical Society. All rights reserved. Printed in the U.S.A.
DAY-SIDE z -BAND EMISSION AND ECCENTRICITY OF WASP-12b∗
Mercedes López-Morales1,8 , Jeffrey L. Coughlin2,9 , David K. Sing3 , Adam Burrows4 , Dániel Apai5 , Justin
C. Rogers1,6 , David S. Spiegel4 , and Elisabeth R. Adams7
1
Carnegie Institution of Washington, Department of Terrestrial Magnetism, 5241 Broad Branch Road NW, Washington, DC 20015, USA; mercedes@dtm.ciw.edu
2 Department of Astronomy, New Mexico State University, Las Cruces, NM 88003, USA
3 Astrophysics Group, School of Physics, University of Exeter, Stocker Road, Exeter, Ex4 4QL, UK
4 Department of Astrophysical Sciences, Princeton University, Peyton Hall, Princeton, NJ 08544, USA
5 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
6 Department of Physics and Astronomy, The Johns Hopkins University, 366 Bloomberg Center, 3400 North Charles Street, Baltimore, MD 21218, USA
7 Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
Received 2009 December 15; accepted 2010 May 5; published 2010 May 20
ABSTRACT
We report the detection of the eclipse of the very hot Jupiter WASP-12b via z -band time-series photometry obtained with the 3.5 m Astrophysical Research Consortium telescope at Apache Point Observatory. We measure
a decrease in flux of 0.082% ± 0.015% during the passage of the planet behind the star. That planetary flux is
equally well reproduced by atmospheric models with and without extra absorbers, and blackbody models with
f 0.585 ± 0.080. It is therefore necessary to measure the planet at other wavelengths to further constrain its
atmospheric properties. The eclipse appears centered at phase φ = 0.5100+0.0072
−0.0061 , consistent with an orbital eccentricity of |e cos ω| = 0.016+0.011
(see
note
at
the
end
of
Section
4).
If
the
orbit
of the planet is indeed eccentric, the
−0.009
large radius of WASP-12b can be explained by tidal heating.
Key words: planetary systems – stars: individual (WASP-12) – techniques: photometric
Online-only material: color figures
In the case of tidal heating, detailed models are now being
developed (e.g., Bodenheimer et al. 2003; Miller et al. 2009;
Ibgui et al. 2009a, 2009b; Ibgui & Burrows 2009) to explain the
inflated radius phenomenon observed in hot Jupiters, of which
WASP-12b, with a radius over 40% larger than predicted by
standard models, is also an extreme case. All models assume that
the planetary orbits are slightly eccentric, and directly measuring
those eccentricities is key not only to test the model hypotheses,
but also to obtain information about the planets’ core mass and
energy dissipation mechanisms (see, e.g., Ibgui et al. 2009a).
Here we present the detection of the eclipse of WASP-12b
in the z band (0.9 μm), which gives the first measurement
of the atmospheric emission of this planet, and the first direct
estimation of its orbital eccentricity. Section 2 summarizes the
observations and analysis of the data. In Section 3, we compare
the emission of the planet to models. The results are discussed
in Section 4.
1. INTRODUCTION
The transiting very hot Jupiter WASP-12b, discovered by
Hebb et al. (2009), has many notable characteristics. With a mass
of 1.41 ± 0.10 MJup and a radius of 1.79 ± 0.09 RJup , WASP-12b
is the planet with the second largest radius reported to date. It is
also the most heavily irradiated planet known, with an incident
stellar flux at the substellar point of over 9 × 109 erg cm−2 s−1 .
In addition, model fits to its observed radial velocity and transit
light curves suggest that the orbit of WASP-12b is slightly
eccentric. All these attributes make WASP-12b one of the best
targets to test current irradiated atmosphere and tidal heating
models for extrasolar planets.
In irradiated atmosphere model studies, WASP-12b is an
extreme case even in the category of highly irradiated gas giants.
Such highly irradiated planets are expected to show thermal
inversions in their upper atmospheric layers (Burrows et al.
2008), although the chemicals responsible for such inversions
remain unknown. TiO and VO molecules, which can act as
strong optical absorbers, have been proposed (Hubeny et al.
2003; Fortney et al. 2008), but Désert et al. (2008) claim that
the concentration of those molecules in planetary atmospheres
is too low (<10−3 to 10−2 times solar). Spiegel et al. (2009)
argue that TiO needs to be at least half the solar abundance to
cause thermal inversions, and very high levels of macroscopic
mixing are required to keep enough TiO in the upper atmosphere
of planets. S2 , S3 , and HS compounds have also recently been
suggested and then questioned as causes of the observed thermal
inversions (Zahnle et al. 2009a, 2009b).
2. OBSERVATIONS AND ANALYSES
We monitored WASP-12 (R.A. (J2000) = 06:30:32.794, decl.
(J2000) = +29:40:20.29, V = 11.7) during two eclipses, and
under photometric conditions, on 2009 February 19 and October
18 UT. An additional attempt on 2009 October 30 UT was
lost due to weather. The data were collected with the SPICam
instrument on the Astrophysical Research Consortium’s 3.5 m
telescope at Apache Point Observatory, using a Sloan Digital
Sky Survey (SDSS) z filter with an effective central wavelength
of ∼0.9 μm. SPICam is a backside-illuminated SITe TK2048E
2048 × 2048 pixel CCD with 24 μm pixels, giving an unbinned
plate scale of 0.14 arcsec per pixel and a field of view of 4.78
arcmin2 . The detector, cosmetically excellent and linear through
the full A/D converter range, was binned 2 × 2, which gives
a gain of 3.35 e− /ADU, a read noise of 1.9 DN pixel−1 , and a
48 s read time.
∗ Based on observations collected with the Apache Point Observatory 3.5 m
telescope, which is owned and operated by the Astrophysical Research
Consortium (ARC).
8 Hubble Fellow.
9 NSF Graduate Research Fellow.
L36
No. 1, 2010
DAY-SIDE z -BAND EMISSION AND ECCENTRICITY OF WASP-12b
On February 19, we monitored WASP-12 from 3:00 to 3:28
UT and from 3:54 to 7:10 UT, losing coverage between 3:28
and 3:54 UT when the star reached a local altitude greater
than 85◦ , the soft limit of the telescope at that time. These
observations yielded 1.20 hr of out-of-eclipse and 2.45 hr of
in-eclipse coverage, at airmasses between 1.005 and 1.412. On
October 18, we extended the altitude soft limit of the telescope
to 87◦ and covered the entire eclipse from 7:05 to 12:45 UT,
yielding 2.73 hr of out-of-eclipse and 2.93 hr of in-eclipse
coverage, with airmasses between 1.001 and 1.801. On both
nights, we defocused the telescope to an FWHM of ∼2 to
reduce pixel sensitivity variation effects, and also to allow for
longer integration times, which minimized scintillation noise
and optimized the duty cycle of the observations. Pointing
changed by less than (x, y) = (4, 7) pixels in the October 18
data set, and by less than (x, y) = (3, 12) pixels on February 19,
with the images for this second night suffering a small gradual
drift in the y direction throughout the night. Integration times
ranged from 10 to 20 s. Taking into account Poisson, readout,
and scintillation noise, the photometric precision on WASP-12
and other bright stars in the images ranged between 0.07% and
0.15% per exposure on February 19, and between 0.05% and
0.09% per exposure on October 18.
The field of view of SPICam was centered at R.A. (J2000) =
06:30:25, decl. (J2000) = +29:42:05 and included WASP-12
and two other isolated stars at R.A. (J2000) = 06:30:31.8, decl.
(J2000) = +29:42:27 and R.A. (J2000) = 06:30:22.6, decl.
(J2000) = +29:44:42, with apparent brightness and B − V and
J − K colors similar to the target. Each night’s data set was
analyzed independently and the results were combined in the
end. The timing information was extracted from the headers of
the images and converted into Heliocentric Julian Days using the
IRAF task setjd, which has been tested to provide sub-second
timing accuracy.
We corrected each image for bias-level and flat-field effects
using standard IRAF routines. Dark current was negligible.
DAOPHOT-type aperture photometry was performed in each
frame. We recorded the flux from the target and the comparison
stars over a wide range of apertures and sky background annuli
around each star. We used apertures between 2 and 35 pixels
in 1 pixel steps during a first preliminary photometry pass, and
0.05 pixel steps in the final photometric extraction. To compute
the sky background around each star we used variable width
annuli, with inner radii between 35 and 60 pixels sampled in
1 pixel steps.
The best aperture and sky annuli combinations were selected
by identifying the most stable (i.e., minimum standard deviation), differential light curves between each comparison and the
target at phases out-of-eclipse.10 In the February 19 data, the
best photometry results from an aperture radius of 14.7 pixel for
both the target and the comparison stars, and sky annuli with
a 52 pixel inner radius and 22 pixel wide. For the October 18
data, 17.9 pixel apertures and sky annuli with a 45 pixel inner
radius and 22 pixel wide produce the best photometry.
The resultant differential light curves between the target
and each comparison contain systematic trends that can be
attributed to either atmospheric effects, such as airmass, seeing,
or sky brightness variations, or to instrumental effects, such
as small changes in the location of the stars on the detector.
Systematics can also be introduced by instrumental temperature
10
We had to iterate on the out-of-eclipse phase limits after finding that the
eclipse was centered at φ = 0.51. Out-of-eclipse was finally defined as phases
φ < 0.45 and φ > 0.57.
L37
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
0.4
0.2
0
-0.2
0.4
0.45
0.5
0.55
0.6
phase
Figure 1. Top: de-trended differential light curves. Open and filled dots show,
respectively, the 2009 February 19 and October 18 UT data. Bottom: combined
light curves binned by a factor of 12. Blue squares correspond to WASP-12 and
black dots to the differential light curve of the two comparison stars. The best-fit
models are shown as solid lines (for e = 0) and dashed lines (for e = 0.057).
Both models produce the same depth and center phase, but the e = 0.057 model
lasts 11.52 minutes longer. We attribute the flux jumps between phases 0.475
and 0.5 to unremoved systematics. Note that, although the systematics appear
in both curves, the trends in each curve are not correlated.
(A color version of this figure is available in the online journal.)
or pressure changes, but those parameters are not monitored
in SPICam. We modeled systematics for each light curve by
fitting linear correlations between each parameter (airmass,
seeing, sky brightness variations, and target position) and the
out-of-eclipse portions of the light curves. All detected trends
are linear and there are no apparent residual color difference
effects. The full light curves are then de-trended using those
correlation fits. In the October 18 data set, airmass effects are
the dominant systematic, introducing a linear baseline trend with
an amplitude in flux of 0.07%. The February 19 data set also
shows systematics with seeing and time with a total amplitude
of also 0.07%. The systematics on this night were modeled
using only the after-eclipse portion of the light curve, and we
consider this data set less reliable that the October 18 one.
The 18 pre-ingress images collected between 3:00 and 3:38 UT
suffer from a ∼50 pixel position shift with respect to the rest
of the images collected that night, which cannot be modeled
using overall out-of-eclipse systematics. We chose not to use
those points in the final analysis. Correlations with the other
parameters listed above are not significant in any of the two data
sets.
Finally, we produce one light curve per night by combining
the de-trended light curves of each comparison. The light
curves are combined by applying a weighted average based
on the Poisson noise of the individual light curve points. The
result is illustrated in Figure 1. The out-of-eclipse scatter of
the combined light curves is 0.11% for the February 19 data
and 0.09% for the October 18 data. De-trending significantly
improves the systematics, but some unidentified residual noise
sources remain, which we have not been able to fully model.
L38
LÓPEZ-MORALES ET AL.
Normalized Flux Histogram
4
z (Normalized χ2)
4
z (Normalized χ2)
40
Vol. 716
3
2
1
0
30
0.00
3
2
1
0
0.04
0.07
0.11
Eclipse Depth (%)
0.14
0.46
0.48
0.50
0.52
Center Phase
0.54
0.56
0.14
3σ
Eclipse depth (%)
0.12
20
0.10
1σ
0.08
0.06
2σ
0.04
3σ
0.48
0.50
0.52
0.54
Center phase
10
0
-0.004
-0.002
0
0.002
0.004
Figure 3. Top: model eclipse one-dimensional cuts through the normalized-χ 2
parameter space for the eclipse depth and center phase. z = 0 gives the best fit
and z = 1 shows the 1σ confidence interval. Bottom: contour plot of the eclipse
depth vs. the center phase, where the 1σ depth error has been fixed to 0.015%.
The best model fit is indicated by the cross symbol at φ = 0.51 and depth =
0.082%, together with 1σ –3σ confidence contours. The star symbol at φ = 0.50
corresponds to a circular orbit.
Differential Flux
Figure 2. Normalized flux histograms of the in-eclipse (dotted red line) and
out-of-eclipse (solid line) portions of the WASP-12 light curve in Figure 1. The
bin width is 0.00082 in differential flux, coincident with the detected eclipse
depth.
(A color version of this figure is available in the online journal.)
2.1. Eclipse Detection and Error Estimation
The two-night combined light curve contains 421 points
between phases 0.413 and 0.596, based on the Hebb et al. (2009)
ephemerides. To establish the presence of the eclipse and its
parameters, we fit the data to a grid of models generated using
the JASMINE code, which combines the Kipping (2008) and
Mandel & Agol (2002) algorithms to produce model light curves
in the general case of eccentric orbits. The models do not include
limb darkening and use as input parameters the orbital period,
stellar and planetary radii, argument of the periastron, orbital
inclination, stellar radial velocity amplitude, and semimajor
axis values derived by Hebb et al. (2009). The eccentricity is
initially assumed to be e = 0, which produces models with a
total eclipse duration of 2.808 hr. The best-fit model is found by
χ 2 minimization with the depth, the central phase of the eclipse,
and the out-of-eclipse differential flux as free parameters.
First, we fit the individual night light curves to ensure that the
eclipse signal is present in each data set. The February 19 data
give an eclipse depth of 0.100% ± 0.023%, while the derived
eclipse depth for the October 18 data is 0.068% ± 0.021%. The
central phases are φ = 0.510 for the first eclipse and φ = 0.508
for the second. We assume that the difference in depth is due
to systematics we have not been able to properly model. The
incomplete eclipse from February 19 might seem more prone
to systematics, but our inspection of both data sets does not
reveal stronger trends in that data set. We therefore combined
the data from both nights, weighting each light curve based on
its out-of-eclipse scatter.
The result of the combined light curve analysis is the detection
of an eclipse with a depth of 0.082% ± 0.015% and centered at
orbital phase φ = 0.51, as shown in Figure 1. The reduced χ 2 of
the fit is 0.952. The error in the eclipse depth is computed using
2
the equation σdepth
= σw2 /N + σr2 , where σw is the scatter per
out-of-eclipse data point and σr2 describes the red noise. The σr
is estimated with the binning technique by Pont et al. (2006) to
be 1.5 × 10−4 when binning on timescales up to the ingress and
egress duration of about 20 minutes.
We investigate to what extent the uncertainties in the system’s
parameters affect our eclipse depth and central phase results.
Varying the impact parameter, planet-to-star ratio, and scale
of the system by 1σ of the reported values in Hebb et al.
(2009), the measured eclipse depth changes only by 0.004%
or 0.27σdepth , while the central phase remains unchanged. Our
result is therefore largely independent of the adopted system
parameters.
We performed three other tests to confirm the eclipse detection in a manner similar to previously reported eclipse results (Deming et al. 2005; Sing & López-Morales 2009; Rogers
et al. 2009). From the average of the 125 out-of-eclipse light
curve data points versus the 228 in-eclipse points (only points
where the planet is fully eclipsed, adopting φ = 0.51 as the central eclipse phase), we measure an eclipse depth of 0.080% ±
0.015%. We further check the detection by producing histograms of the normalized light curve flux distribution in the
in-eclipse and out-of-eclipse portions of the light curve. The
result, illustrated in Figure 2, shows how the flux distribution
of in-eclipse points is shifted by 0.00082 with respect to the
out-of-eclipse flux distribution, centered at zero. The results of
the last test, where we use a new set of eclipse models with
a duration corresponding to e = 0.057, fix the out-of-eclipse
baseline to zero, and leave both depth and central phase of the
eclipse as free parameters, are shown in Figure 3. The two top
panels in the figure show one-dimensional cuts of each parameter through the z (normalized χ 2 ) space, where z = 0 gives the
best-fit model and z = 1 defines the 1σ confidence interval of the
result (see the definition of z in Section 3 of López-Morales &
Bonanos 2008; Behr 2003). However, inspection of the eclipse
depth in Figure 1 reveals that the 1σ errors from this method
(±0.036%) are too large. To estimate more realistic errors for
the central phase, we generate contour plots (bottom panel in
Figure 3), where the 1σ eclipse depth error has been fixed to
the 0.015% value derived above. The resultant center phase is
DAY-SIDE z -BAND EMISSION AND ECCENTRICITY OF WASP-12b
No. 1, 2010
L39
0.5
1σ
0.3
0.2
1σ
2σ
Bond albedo AB
0.4
2σ
0.1
0.0
0.2
0.3
0.4
0.5
0.6
Heat redistribution factor (f)
0.7
0.8
Figure 4. Values of AB and f that reproduce the observed z -band eclipse depth
of WASP-12b, assuming the planet emits as a blackbody. The shaded area
highlights the region of allowed f values (1/4–2/3). The short and long dashed
lines delimit, respectively, the 1σ and 2σ confidence regions of the result.
φ = 0.5100+0.0072
−0.0061 . We also applied prayer-bead, bootstrapping,
and Markov Chain Monte Carlo (MCMC) error analysis techniques (Gillon et al. 2007; Southworth 2008) to estimate the
errors in the central phase of the eclipse. The MCMC analysis contained 2.85 × 106 links, and we adopted the 1.5 × 10−4
photometric error (∼1.6 times the formal error), given by the
Pont et al. (2006) binning technique. All of these give central
phases within φ = 0.5100+0.0030
−0.0036 . The larger error in the central
phase given by the normalized χ 2 method suggests the presence
of correlated noise in the data, which the other methods might
not be correctly accounting for. We therefore adopt these larger
errorbars in our final estimation of the central phase.
2.2. Eccentricity
The eccentricity e of WASP-12b was calculated from the
measured central phase shift value using Equation (6) from
Wallenquist (1950),
e cos ω =
π (t2 − t1 − P /2)
,
P
1 + csc2 i
(1)
where P, i, and ω are, respectively, the orbital period, inclination,
and periastron angle of the system, and t2 − t1 is the time
difference between transit and eclipse. In our case, t2 − t1 =
0.51P . Using the values of P, i, and ω from Hebb et al. (2009),
we derive e = 0.057+0.040
−0.034 , which agrees with the non-zero
eccentricity result reported by these authors. This eccentricity
can be, in principle, explained if (1) the system is too young
to have already circularized, (2) there are additional bodies in
the system pumping the eccentricity of WASP-12b, or (3) the
tidal dissipation factor QP (Goldreich 1963) of WASP-12b is
several orders of magnitude larger than Jupiter’s, estimated to
be between 6 × 104 and 2 × 106 (Yoder & Peale 1981).
3. COMPARISON WITH ATMOSPHERIC MODELS
We compare the observed z -band flux of WASP-12b to
simple blackbody models and to expectedly more realistic radiative–convective models of irradiated planetary atmospheres in chemical equilibrium, following the same procedure
described in Rogers et al. (2009). The results are shown in
Figures 4 and 5.
Figure 5. Comparison of the eclipse depth (planet-to-star flux ratio) to models.
The green line shows the AB = 0.4, f = 2/3 blackbody model from Figure 4.
The blue and red lines show, respectively, the best-fit model for an atmosphere
with no extra absorber, and with an extra absorber of opacity κ between 0.43
and 1.0 μm. The black thin line at the bottom indicates the SPICam plus SDSS
z -band filter response. See Section 3 for more details.
(A color version of this figure is available in the online journal.)
In the simplistic blackbody approximation, a 0.082% ±
0.015% deep eclipse corresponds to a z -band brightness temperature of Tz ∼ 3028+99
−110 K, slightly lower than the planet’s
equilibrium temperature of Tp ∼ 3129 K assuming zero Bond
albedo (AB = 0) and no energy reradiation (f = 2/3; see
López-Morales & Seager 2007). However, when the thermal
and reflected flux of the planet are included, different combinations of AB and f can yield the same eclipse depth, as illustrated
in Figure 4. From that figure we can constrain the energy redistribution factor to f 0.585 ± 0.080, but the albedo is not well
constrained. Assuming a maximum AB 0.4, the temperature
of the day-side of WASP-12b is Tp > 2707 K.
The more realistic atmospheric models are derived from selfconsistent coupled radiative transfer and chemical equilibrium
calculations, based on the models described in Sudarsky et al.
(2000, 2003), Hubeny et al. (2003), and Burrows et al. (2005,
2006, 2008; see Rogers et al. 2009, for details). We generate
models with and without thermal inversion layers, by adding
an unidentified optical absorber between 0.43 and 1.0 μm,
with different levels of opacity κ . The opacity of the absorber
varies parabolically with frequency, with a peak value of κ =
0.25 cm2 g−1 . As Figure 5 shows, models with and without
extra absorbers produce similar fits to the observed z -band
flux. The best model without absorber has Pn = 0.3.11 The
best model with an extra absorber has Pn = 0.1 and κe =
0.1 cm2 g−1 . Observations at other wavelengths are necessary
to further constrain the models.
11 P = 0 and P = 0.5 correspond, respectively, to f = 2/3 and f = 1/4,
n
n
however, there is no well-defined Pn –f relation for intermediate values since
the physical models account for atmospheric parameters (e.g., pressure,
opacity) in a way different from blackbody models.
L40
LÓPEZ-MORALES ET AL.
4. DISCUSSION AND CONCLUSIONS
This first detection of the eclipse of WASP-12b agrees with
the slight eccentricity of the planet’s orbit found by Hebb
et al. (2009), and places initial constraints to its atmospheric
characteristics.
The presence of other bodies in the system can be tested via
radial velocity or transit timing variation observations, although
the current radial velocity curve by Hebb et al. (2009) shows
no evidence of additional planets, unless they are in very long
orbits.
One would expect that if extra absorbers are present in the
upper atmosphere of the planet in gaseous form, they might give
rise to thermal inversion layers. However, as Figure 5 illustrates,
the observed 0.9 μm eclipse depth can be fit equally well by
a model without extra absorbers. Additional observations at
longer wavelengths, especially longer than ∼4.0 μm, will break
that model degeneracy. Observations at wavelengths below ∼0.6
μm will also place better constraints on AB .
M.L.-M. acknowledges support from NASA through Hubble
Fellowship grant HF-01210.01-A/HF-51233.01 awarded by the
STScI, which is operated by the AURA, Inc. for NASA, under
contract NAS5-26555. J.L.C. acknowledges support from an
NSF Graduate Research Fellowship. A.B. is supported in part
by NASA grant NNX07AG80G. D.A. and J.C.R. are grateful
for the support from STScI Director’s Discretionary Research
Fund D0101.90131. This work has been supported by NSF’s
grant AST-0908278.
Note added. While this Letter was in the final revision stages,
two new secondary eclipse observations from Spitzer were reported by Campo et al. (2010). They find secondary eclipse
central phases consistent with a circular orbit. We have carefully reviewed our analysis and still arrive at a slightly eccentric
orbit, although the result is only significant at the 1.4σ –1.6σ
confidence level. Possible explanations proposed by Campo
Vol. 716
et al. (2010) for the measured eccentricity difference are orbital precession or wavelength-dependent brightness variations
across the surface of the planet that would shift the center of the
eclipse. A similar effect has been recently suggested by Swain
et al. (2010) on the surface of HD189733b. Further observations
are needed to establish whether this discrepancy is a data artifact
or a real effect.
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